A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains

Fuente: arXiv
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Auteurs principaux: Qian, Yixiao, Li, Weizhen, Tan, Yan, Zhang, Qinghai
Format: Preprint
Publié: 2024
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author Qian, Yixiao
Li, Weizhen
Tan, Yan
Zhang, Qinghai
author_facet Qian, Yixiao
Li, Weizhen
Tan, Yan
Zhang, Qinghai
contents We propose a fourth-order cut-cell method for solving Poisson's equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable to arbitrarily complex geometries, (b) high order discretization, (c) optimal complexity. Feature (a) is achieved by Yin space, which is a mathematical model for three-dimensional continua. Feature (b) is accomplished by poised lattice generation (PLG) algorithm, which finds stencils near the irregular boundary for polynomial fitting. Besides, for feature (c), we design a modified multigrid solver whose complexity is theoretically optimal by applying nested dissection (ND) ordering method.
format Preprint
id arxiv_https___arxiv_org_abs_2410_05865
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains
Qian, Yixiao
Li, Weizhen
Tan, Yan
Zhang, Qinghai
Numerical Analysis
We propose a fourth-order cut-cell method for solving Poisson's equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable to arbitrarily complex geometries, (b) high order discretization, (c) optimal complexity. Feature (a) is achieved by Yin space, which is a mathematical model for three-dimensional continua. Feature (b) is accomplished by poised lattice generation (PLG) algorithm, which finds stencils near the irregular boundary for polynomial fitting. Besides, for feature (c), we design a modified multigrid solver whose complexity is theoretically optimal by applying nested dissection (ND) ordering method.
title A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains
topic Numerical Analysis
url https://arxiv.org/abs/2410.05865